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Benjamin, Lund
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Simple Proofs for Furstenberg Sets Over Finite Fields

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Title
Simple Proofs for Furstenberg Sets Over Finite Fields
Author(s)
Dhar, Manik; Dvir, Zeev; Ben Lund
Publication Date
2021-10-14
Journal
DISCRETE ANALYSIS, v.2021, no.22, pp.1 - 16
Publisher
ALLIANCE DIAMOND OPEN ACCESS JOURNALS
Abstract
A (k, m)-Furstenberg set S subset of F-q(n) over a finite field is a set that has at least m points in common with a k-flat in every direction. The question of determining the smallest size of such sets is a natural generalization of the finite field Kakeya problem. The only previously known bound for these sets is due to Ellenberg-Erman [6] and requires sophisticated machinery from algebraic geometry. In this work we give new, completely elementary and simple proofs that significantly improve the known bounds. Our main result relies on an equivalent formulation of the problem using the notion of min-entropy, which could be of independent interest.
URI
https://pr.ibs.re.kr/handle/8788114/11033
DOI
10.19086/da.29067
ISSN
2397-3129
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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